Back to security Sample Clauses

Back to security. But is it enough? Can the adversary do other things other than simply solve Discrete Log? The answer is that we do not know. We do not know how to prove the protocol only by Discrete Logarithm. In fact we know of groups that Discrete Log is hard, but still this protocol won’t be secure. What is the view of the adversary? (what does he see) The view of the adversary is: 1. G, g, q. 2. gx (for random x). 3. gy (for random y). And in this case, that is all. The goal of the adversary is to find gxy. We are going to define the game: DHKE-Game Challenger Adversary (G, g, q) ← GroupGen 1k x, y ∈ Zq (G, g, q) , gx, gy Choose at random: b ∈ {0, 1} If b = 0 then z = x · y If b = 1 then z ∈ Zq gz b′ Adversary wins if b′ = b We want to evaluate the advantage of the adversary: DHKE − Adv [A] (k) = Randomness of Challenger and Adversary Pr A 1 wins − 1/2 = Pr 2 A k = 1 | b = 0 − Pr A 1k = 1 | b = 1 We do not know how to prove security for this protocol, but we use this protocol as a base line for other constructions. We define an Hardness Assumption which encapsulates the hardness of this protocol. We assume Decisional Xxxxxx-Xxxxxxx (DDH). The assumption, with respect to GroupGen, will yield that the protocol is secure. In order to define it formally we need some definitions:
Sample 1
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